[JdeBP]

You're being misled by the misleading marketing name, too. This isn't the Bourne Again shell at all. It's a "personality" subsystem that lets one run Linux binaries directly on top of the Windows NT kernel. One of those binaries may well be the Bourne Again shell, but that is largely irrelevant. The Bourne Again shell binary comes from Canonical (or from RedHat if, say, you choose to experiment with running Fedora on the Windows Subsystem for Linux).

The part that comes from Microsoft is the Windows Subsystem for Linux, and of course the Windows NT kernel beneath it (and the Win32 subsystem alongside it). Unless something has changed recently, that is not open source.